Computer Methods for Discrete Logarithm Problem: a Cryptographic Perspective

Compution of discrete logarithm is of great interest because of its relevance to public key cryptography. It is believed to be a hard problem because no polynomial time solution has been found. One of the generic algorithm in computing discrete logarithm is Pollard rho algorithm (and its derivatives). The algorithm depend on the ”birthday paradox” idea and makes a pseudo-random walk in finite abelian group. If the group is of order n, the algorithm has expected running time O( √ n), provided the pseudo-random walk behaves like a genuine random walk. Furthermore, storage requirements are minimal. In some cases such as the group of an elliptic curve, the algorithm is the fastest known method currently.